Balogh–Bollobás asymptotic conjecture for bootstrap percolation in the hypercube

Let $r\geq 3$ be fixed, and let $Q_d$ be the graph with vertex set $\{0,1\}^d$ in which two vertices are adjacent when they differ in exactly one coordinate. For the $r$-neighbour bootstrap process on $Q_d$, let $m(Q_d,r)$ denote the minimum cardinality of an initial set that percolates. Balogh–Bollobás conjecture. As $d\to\infty$,

$$m(Q_d,r)=\frac{1+o(1)}{r}\binom{d}{r-1}.$$

The conjecture gives the asymptotic minimum size of a percolating set in the high-dimensional hypercube. The source paper states that it proves this conjecture, so its status is solved.